There is growing interest in digital twins for engineering and science applications to enable real-time monitoring, prediction, optimization, and cost-free what-if experimentation. Different from computer aided engineering simulations, two defining features of digital twins are capability of assimilating physical world data and real time simulation speed. However, data assimilation algorithms, such as Markov chain Monte Carlo (MCMC) and Ensemble Kalman Filter (EnKF) are computationally expensive. Deep learning-based surrogate models, such as DeepONet and Fourier Neural Operator, have demonstrated the potential to accelerate them [4, 5]. These data-driven approaches often fail to conserve physical quantities. Models like Physics-Informed Neural Networks and Physics-Informed Neural Operators attempt to address this issue [2,6], they are sometimes challenging to train for complex problems with multiple loss constraints. We proposed a hybrid two-level sampling method to accelerate the computation of statistical mean and variance in Bayesian inversion and filtering problems with an accuracy comparable to the numerical approach [7]. We will present our computational framework for MCMC [7] and a new extension to EnKF. Inspired by the classical numerical multilevel approach [1, 3, 8], we generate samples at two parallel levels, one with a deep learning surrogate model and the other with a numerical model. The GPU-accelerated deep learning surrogate model will generate a large number of samples, thus reducing the sampling error. And another smaller ensemble of numerical samples to correct the bias error from the primary ensemble generated with non-physical constrained AI surrogate model. We will demonstrate our approach through numerical experiments with MCMC [7] as well as new results for hybrid two level EnKF. In conclusion, our hybrid method allows the usage of state-of-the-art deep learning models for practical application prior to more robust physics informed machine learning methods becoming available.